Multiscale Process Coupling by Adaptive Fractional Stepping: An In-Situ Combustion Model
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AbstractWe propose a time-stepping methodology for in-situ combustion simulation that is designed specifically to accommodate the various physical sub-processes, including conduction, advection, and kinetics, that have widely varying time-scales. The approach combines operator splitting with fractional time-stepping. The method is applied to a scaled form of the governing equations. We derived seven independent scaling parameters in the in-situ combustion process, representing ratios of heat capacity, mass transfer and heats of reaction.We provide a proof of concept for one particular splitting and fractional step method that we found to be intuitive. In each time-step of this scheme, we solve the pressure equation semi-implicitly. Conservative accumulation treatment is assured by elimination at the Jacobian level. This is followed by an explicit solve for temperature, where a second elimination is performed to de-couple accumulation terms from the remaining concentration equations. The concentration equations are then integrated in a fractional- step, additive-splitting fashion. This means that reactions are separated numerically from the concentration advection- reaction equations. The overall solution for concentrations is obtained by performing a sequence of solves for reactions alternating with pure advection. A local fractional time-step size for either sub-process is introduced, and may be varied according to the local physics. Finally the global time-step solution is composed in an accurate fashion out of the sub-process solves.To test the method a couple of test problems were designed for which the parameters are given in full detail so that it can be used for inter-code comparisons.
